Answer to Question #98294 in Discrete Mathematics for Ahmed

Question #98294
Calculate (by hand) the appropriate truth table to prove or disprove the following:
(p → q) ∧ (¬p → r) ⇒ (q ∨ r)
If it is invalid, give a counterexample; otherwise, explain why it is valid.
1
Expert's answer
2019-11-11T10:42:30-0500



As, [(pq)(¬pr)](qr)[(p → q) ∧ (¬p → r)] \to (q ∨ r) is a Tautology (always true) ;

Thus; the implication holds.

(pq)(¬pr)(qr)\therefore (p → q) ∧ (¬p → r) ⇒ (q ∨ r)

It is valid as the condtional is a Tautolgy; hece the Implication holds.


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